(New throughout) NEW YORK, June 1 (Reuters) - The U.S. Treasury yields were set to close the New York session on Tuesday mostly flat, ultimately little moved by manufacturing data released earlier which showed strong demand in the sector, even as industry faces labor and raw material shortages. The Institute for Supply Management (ISM) said on Tuesday its index of national factory activity increased in May as pent-up demand, driven by a reopening economy and fiscal stimulus, boosted orders. But strong demand has strained supply chains. And the coronavirus has disrupted labor at manufacturers and their suppliers, leading to raw material shortages across industries. The benchmark 10-year yield, a proxy for the market’s view on the health of the economy, was last 2.2 basis points higher on the day at 1.615%. The two-year yield , which reflects expectations of interest-rate rises, was up less than half a basis point on the day at 0.147% The manufacturing data earlier in the day had steepened the yield curve by the most in a week, reflecting expectations that the Federal Reserve would keep interest rates on hold, even as the reopening economy boosts growth. The yield curve was still modestly steeper on Tuesday afternoon, but had narrowed from earlier highs as the market digested the manufacturing data. “All of this data is positive for continued manufacturing growth going forward but the supply chain issues are a constraint for now,” said Ellis Phifer, managing director at Raymond James. Every move on Tuesday was modest, however, as investors held off from making big moves ahead of Friday’s closely watched U.S. jobs report. “This morning’s ISM as well as tomorrow’s Beige Book and Thursday’s ADP report will function as little more than imperfect proxies for the Bureau of Labor Statistics employment release. While any clues on the sustainability of the recent bout of inflation within the interim data will be notable... the direction in U.S. rates will ultimately come down to the non-farm payrolls print,” said Ian Lyngen, head of U.S. rates strategy at BMO Capital Markets. Lyngen said this despite also acknowledging that the last two employment reports have had very little lasting effect on Treasury yields. The Federal Reserve has said it does not plan to raise interest rates until the economy has achieved maximum employment. While economic data has shown signs that reopening is driving growth, the labor market recovery has been less established. Despite a strong report in March, April’s jobs numbers fell well short of estimates. (Reporting by Kate Duguid; Editing by Andrea Ricci and Chizu Nomiyama)